// MersenneTwister.h
// Mersenne Twister random number generator -- a C++ class MTRand
// Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
// Richard J. Wagner  v1.1  28 September 2009  wagnerr@umich.edu

// The Mersenne Twister is an algorithm for generating random numbers.  It
// was designed with consideration of the flaws in various other generators.
// The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
// are far greater.  The generator is also fast; it avoids multiplication and
// division, and it benefits from caches and pipelines.  For more information
// see the inventors' web page at
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html

// Reference
// M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
// Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
// Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.

// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
// Copyright (C) 2000 - 2009, Richard J. Wagner
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// 
//   1. Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//
//   2. Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in the
//      documentation and/or other materials provided with the distribution.
//
//   3. The names of its contributors may not be used to endorse or promote 
//      products derived from this software without specific prior written 
//      permission.
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.

// The original code included the following notice:
// 
//     When you use this, send an email to: m-mat@math.sci.hiroshima-u.ac.jp
//     with an appropriate reference to your work.
// 
// It would be nice to CC: wagnerr@umich.edu and Cokus@math.washington.edu
// when you write.

// Minor modifications made by Michele Bosi:
// - MTRand renamed MersenneTwister.
// - MersenneTwister derived from vl::Object.
// - MersenneTwister included in vl namespace to avoid collisions with other MersenneTwister versions.
// - prepended VL_ to MERSENNETWISTER_H to avoid collisions with other MersenneTwister headers.
// - fixed minor warnings.

#ifndef VL_MERSENNETWISTER_H
#define VL_MERSENNETWISTER_H

// Not thread safe (unless auto-initialization is avoided and each thread has
// its own MersenneTwister object)

#include <iostream>
#include <climits>
#include <cstdio>
#include <ctime>
#include <cmath>
#include <vlCore/Object.hpp>

namespace vl
{
  //-------------------------------------------------------------------------
  class MersenneTwister;
  //-------------------------------------------------------------------------
  VLCORE_EXPORT MersenneTwister* defMersenneTwister();
  VLCORE_EXPORT void setDefMersenneTwister(MersenneTwister*);
  //-------------------------------------------------------------------------
  class MersenneTwister: public Object
  {
  // Data
  public:
	  typedef unsigned long uint32;  // unsigned integer type, at least 32 bits
	
	  enum { N = 624 };       // length of state vector
	  enum { SAVE = N + 1 };  // length of array for save()

  protected:
	  enum { M = 397 };  // period parameter
	
	  uint32 state[N];   // internal state
	  uint32 *pNext;     // next value to get from state
	  int left;          // number of values left before reload needed

  // Methods
  public:
	  MersenneTwister( const uint32 oneSeed );  // initialize with a simple uint32
	  MersenneTwister( uint32 *const bigSeed, uint32 const seedLength = N );  // or array
	  MersenneTwister();  // auto-initialize with /dev/urandom or time() and clock()
	  MersenneTwister( const MersenneTwister& o );  // copy
	
	  // Do NOT use for CRYPTOGRAPHY without securely hashing several returned
	  // values together, otherwise the generator state can be learned after
	  // reading 624 consecutive values.
	
	  // Access to 32-bit random numbers
	  uint32 randInt();                     // integer in [0,2^32-1]
	  uint32 randInt( const uint32 n );     // integer in [0,n] for n < 2^32
	  double rand();                        // real number in [0,1]
	  double rand( const double n );        // real number in [0,n]
	  double randExc();                     // real number in [0,1)
	  double randExc( const double n );     // real number in [0,n)
	  double randDblExc();                  // real number in (0,1)
	  double randDblExc( const double n );  // real number in (0,n)
	  double operator()();                  // same as rand()
	
	  // Access to 53-bit random numbers (capacity of IEEE double precision)
	  double rand53();  // real number in [0,1)
	
	  // Access to nonuniform random number distributions
	  double randNorm( const double mean = 0.0, const double stddev = 1.0 );
	
	  // Re-seeding functions with same behavior as initializers
	  void seed( const uint32 oneSeed );
	  void seed( uint32 *const bigSeed, const uint32 seedLength = N );
	  void seed();
	
	  // Saving and loading generator state
	  void save( uint32* saveArray ) const;  // to array of size SAVE
	  void load( uint32 *const loadArray );  // from such array
	  friend std::ostream& operator<<( std::ostream& os, const MersenneTwister& mtrand );
	  friend std::istream& operator>>( std::istream& is, MersenneTwister& mtrand );
	  MersenneTwister& operator=( const MersenneTwister& o );

  protected:
	  void initialize( const uint32 oneSeed );
	  void reload();
	  uint32 hiBit( const uint32 u ) const { return u & 0x80000000UL; }
	  uint32 loBit( const uint32 u ) const { return u & 0x00000001UL; }
	  uint32 loBits( const uint32 u ) const { return u & 0x7fffffffUL; }
	  uint32 mixBits( const uint32 u, const uint32 v ) const
		  { return hiBit(u) | loBits(v); }
	  uint32 magic( const uint32 u ) const
		  { return loBit(u) ? 0x9908b0dfUL : 0x0UL; }
	  uint32 twist( const uint32 m, const uint32 s0, const uint32 s1 ) const
		  { return m ^ (mixBits(s0,s1)>>1) ^ magic(s1); }
	  static uint32 hash( time_t t, clock_t c );
  };

  // Functions are defined in order of usage to assist inlining

  inline MersenneTwister::uint32 MersenneTwister::hash( time_t t, clock_t c )
  {
	  // Get a uint32 from t and c
	  // Better than uint32(x) in case x is floating point in [0,1]
	  // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)
	
	  static uint32 differ = 0;  // guarantee time-based seeds will change
	
	  uint32 h1 = 0;
	  unsigned char *p = (unsigned char *) &t;
	  for( size_t i = 0; i < sizeof(t); ++i )
	  {
		  h1 *= UCHAR_MAX + 2U;
		  h1 += p[i];
	  }
	  uint32 h2 = 0;
	  p = (unsigned char *) &c;
	  for( size_t j = 0; j < sizeof(c); ++j )
	  {
		  h2 *= UCHAR_MAX + 2U;
		  h2 += p[j];
	  }
	  return ( h1 + differ++ ) ^ h2;
  }

  inline void MersenneTwister::initialize( const uint32 seed )
  {
	  // Initialize generator state with seed
	  // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
	  // In previous versions, most significant bits (MSBs) of the seed affect
	  // only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
	  uint32 *s = state;
	  uint32 *r = state;
	  int i = 1;
	  *s++ = seed & 0xffffffffUL;
	  for( ; i < N; ++i )
	  {
		  *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
		  r++;
	  }
  }

  inline void MersenneTwister::reload()
  {
	  // Generate N new values in state
	  // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
	  static const int MmN = int(M) - int(N);  // in case enums are unsigned
	  uint32 *p = state;
	  int i;
	  for( i = N - M; i--; ++p )
		  *p = twist( p[M], p[0], p[1] );
	  for( i = M; --i; ++p )
		  *p = twist( p[MmN], p[0], p[1] );
	  *p = twist( p[MmN], p[0], state[0] );
	
	  left = N, pNext = state;
  }

  inline void MersenneTwister::seed( const uint32 oneSeed )
  {
	  // Seed the generator with a simple uint32
	  initialize(oneSeed);
	  reload();
  }

  inline void MersenneTwister::seed( uint32 *const bigSeed, const uint32 seedLength )
  {
	  // Seed the generator with an array of uint32's
	  // There are 2^19937-1 possible initial states.  This function allows
	  // all of those to be accessed by providing at least 19937 bits (with a
	  // default seed length of N = 624 uint32's).  Any bits above the lower 32
	  // in each element are discarded.
	  // Just call seed() if you want to get array from /dev/urandom
	  initialize(19650218UL);
	  int i = 1;
	  uint32 j = 0;
	  int k = ( N > seedLength ? (int)N : (int)seedLength );
	  for( ; k; --k )
	  {
		  state[i] =
		  state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
		  state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
		  state[i] &= 0xffffffffUL;
		  ++i;  ++j;
		  if( i >= N ) { state[0] = state[N-1];  i = 1; }
		  if( j >= seedLength ) j = 0;
	  }
	  for( k = N - 1; k; --k )
	  {
		  state[i] =
		  state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
		  state[i] -= i;
		  state[i] &= 0xffffffffUL;
		  ++i;
		  if( i >= N ) { state[0] = state[N-1];  i = 1; }
	  }
	  state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
	  reload();
  }

  inline void MersenneTwister::seed()
  {
	  // Seed the generator with an array from /dev/urandom if available
	  // Otherwise use a hash of time() and clock() values
	
	  // First try getting an array from /dev/urandom
	  FILE* urandom = fopen( "/dev/urandom", "rb" );
	  if( urandom )
	  {
		  uint32 bigSeed[N];
		  uint32 *s = bigSeed;
		  int i = N;
		  bool success = true;
		  while( success && i-- )
			  success = fread( s++, sizeof(uint32), 1, urandom ) != 0;
		  fclose(urandom);
		  if( success ) { seed( bigSeed, N );  return; }
	  }
	
	  // Was not successful, so use time() and clock() instead
	  seed( hash( time(NULL), clock() ) );
  }

  inline MersenneTwister::MersenneTwister( const uint32 oneSeed )
	  { seed(oneSeed); }

  inline MersenneTwister::MersenneTwister( uint32 *const bigSeed, const uint32 seedLength )
	  { seed(bigSeed,seedLength); }

  inline MersenneTwister::MersenneTwister()
	  { seed(); }

  inline MersenneTwister::MersenneTwister( const MersenneTwister& o ): Object(o)
  {
	  const uint32 *t = o.state;
	  uint32 *s = state;
	  int i = N;
	  for( ; i--; *s++ = *t++ ) {}
	  left = o.left;
	  pNext = &state[N-left];
  }

  inline MersenneTwister::uint32 MersenneTwister::randInt()
  {
	  // Pull a 32-bit integer from the generator state
	  // Every other access function simply transforms the numbers extracted here
	
	  if( left == 0 ) reload();
	  --left;
	
	  uint32 s1;
	  s1 = *pNext++;
	  s1 ^= (s1 >> 11);
	  s1 ^= (s1 <<  7) & 0x9d2c5680UL;
	  s1 ^= (s1 << 15) & 0xefc60000UL;
	  return ( s1 ^ (s1 >> 18) );
  }

  inline MersenneTwister::uint32 MersenneTwister::randInt( const uint32 n )
  {
	  // Find which bits are used in n
	  // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
	  uint32 used = n;
	  used |= used >> 1;
	  used |= used >> 2;
	  used |= used >> 4;
	  used |= used >> 8;
	  used |= used >> 16;
	
	  // Draw numbers until one is found in [0,n]
	  uint32 i;
	  do
		  i = randInt() & used;  // toss unused bits to shorten search
	  while( i > n );
	  return i;
  }

  inline double MersenneTwister::rand()
	  { return double(randInt()) * (1.0/4294967295.0); }

  inline double MersenneTwister::rand( const double n )
	  { return rand() * n; }

  inline double MersenneTwister::randExc()
	  { return double(randInt()) * (1.0/4294967296.0); }

  inline double MersenneTwister::randExc( const double n )
	  { return randExc() * n; }

  inline double MersenneTwister::randDblExc()
	  { return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0); }

  inline double MersenneTwister::randDblExc( const double n )
	  { return randDblExc() * n; }

  inline double MersenneTwister::rand53()
  {
	  uint32 a = randInt() >> 5, b = randInt() >> 6;
	  return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
  }

  inline double MersenneTwister::randNorm( const double mean, const double stddev )
  {
	  // Return a real number from a normal (Gaussian) distribution with given
	  // mean and standard deviation by polar form of Box-Muller transformation
	  double x, y, r;
	  do
	  {
		  x = 2.0 * rand() - 1.0;
		  y = 2.0 * rand() - 1.0;
		  r = x * x + y * y;
	  }
	  while ( r >= 1.0 || r == 0.0 );
	  double s = sqrt( -2.0 * log(r) / r );
	  return mean + x * s * stddev;
  }

  inline double MersenneTwister::operator()()
  {
	  return rand();
  }

  inline void MersenneTwister::save( uint32* saveArray ) const
  {
	  const uint32 *s = state;
	  uint32 *sa = saveArray;
	  int i = N;
	  for( ; i--; *sa++ = *s++ ) {}
	  *sa = left;
  }

  inline void MersenneTwister::load( uint32 *const loadArray )
  {
	  uint32 *s = state;
	  uint32 *la = loadArray;
	  int i = N;
	  for( ; i--; *s++ = *la++ ) {}
	  left = *la;
	  pNext = &state[N-left];
  }

  inline std::ostream& operator<<( std::ostream& os, const MersenneTwister& mtrand )
  {
	  const MersenneTwister::uint32 *s = mtrand.state;
	  int i = mtrand.N;
	  for( ; i--; os << *s++ << "\t" ) {}
	  return os << mtrand.left;
  }

  inline std::istream& operator>>( std::istream& is, MersenneTwister& mtrand )
  {
	  MersenneTwister::uint32 *s = mtrand.state;
	  int i = mtrand.N;
	  for( ; i--; is >> *s++ ) {}
	  is >> mtrand.left;
	  mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
	  return is;
  }

  inline MersenneTwister& MersenneTwister::operator=( const MersenneTwister& o )
  {
	  if( this == &o ) return (*this);
	  const uint32 *t = o.state;
	  uint32 *s = state;
	  int i = N;
	  for( ; i--; *s++ = *t++ ) {}
	  left = o.left;
	  pNext = &state[N-left];
	  return (*this);
  }

}

#endif  // MERSENNETWISTER_H

// Change log:
//
// v0.1 - First release on 15 May 2000
//      - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
//      - Translated from C to C++
//      - Made completely ANSI compliant
//      - Designed convenient interface for initialization, seeding, and
//        obtaining numbers in default or user-defined ranges
//      - Added automatic seeding from /dev/urandom or time() and clock()
//      - Provided functions for saving and loading generator state
//
// v0.2 - Fixed bug which reloaded generator one step too late
//
// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
//
// v0.4 - Removed trailing newline in saved generator format to be consistent
//        with output format of built-in types
//
// v0.5 - Improved portability by replacing static const int's with enum's and
//        clarifying return values in seed(); suggested by Eric Heimburg
//      - Removed MAXINT constant; use 0xffffffffUL instead
//
// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
//      - Changed integer [0,n] generator to give better uniformity
//
// v0.7 - Fixed operator precedence ambiguity in reload()
//      - Added access for real numbers in (0,1) and (0,n)
//
// v0.8 - Included time.h header to properly support time_t and clock_t
//
// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
//      - Allowed for seeding with arrays of any length
//      - Added access for real numbers in [0,1) with 53-bit resolution
//      - Added access for real numbers from normal (Gaussian) distributions
//      - Increased overall speed by optimizing twist()
//      - Doubled speed of integer [0,n] generation
//      - Fixed out-of-range number generation on 64-bit machines
//      - Improved portability by substituting literal constants for long enum's
//      - Changed license from GNU LGPL to BSD
//
// v1.1 - Corrected parameter label in randNorm from "variance" to "stddev"
//      - Changed randNorm algorithm from basic to polar form for efficiency
//      - Updated includes from deprecated <xxxx.h> to standard <cxxxx> forms
//      - Cleaned declarations and definitions to please Intel compiler
//      - Revised twist() operator to work on ones'-complement machines
//      - Fixed reload() function to work when N and M are unsigned
//      - Added copy constructor and copy operator from Salvador Espana
